Question

5.36. (a) In a group of 23 strangers, what is the probability that at least two of bout if there are 40 strangers? In a group them have the same birthday? How a of 200 strangers, what is the probability that one of them has the same birthday as your birthday? (Hint. See the discussion in Sect. 5.4.1.) (b) Suppose that there are N days in a year (where N could be any number) and that there are n people. Develop a general formula, analogous to (5.28), for the probability that at least two of them have the same birthday. (Hint. Do a cal- culation similar to the proof of (5.28) in the collision theorem (Theorem 5.38), but note that the formula is a bit different because the birthdays are being selected from a single list of N days.) (c) Find a lower bound of the form Pr(at least one match) 2 1 -e-(some function of n and N) for the probability in (b), analogous to the estimate (5.29).

Answer 1

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N' dan m people in a yeas Psge No. Total no. 2 2- n(n- NI same bintthd